Analysis filter bank and computing procedure thereof, audio frequency shifting system, and audio frequency shifting procedure

ABSTRACT

An analysis filter bank corresponding to a plurality of sub-bands, comprising: multiple sub-filters with different center frequencies which perform multiple complex-type first-order infinite impulse response filtering operations on an audio input signal to generate multiple sub-filter signals; a first set of binomial combiners, each of which performs a weighted-sum operation on a first number of the sub-filter signals with a first set of binomial weights to generate one of multiple sub-band signals; a second set of binomial combiners, each of which performs a weighted-sum operation on a second number of the sub-filter signals with a second set of binomial weights to generate one of multiple lower sub-band-edge signals or one of multiple higher sub-band-edge signals; and multiple envelope detection with decimation devices, which perform multiple envelope detection with decimation operations on the sub-band signals, the lower sub-band-edge signals, and the higher sub-band-edge signals to generate multiple fine spectrums.

TECHNICAL FILED

The present invention relates to the field of audio signal processingand frequency shifting processing, and particularly relates to ananalysis filter bank and computing procedure thereof, an audio frequencyshifting system and an audio frequency shifting procedure based on theanalysis filter bank and computing procedure thereof.

BACKGROUND

Frequency shifting is a common type of audio processing, which shiftseach frequency component of an audio input signal by a specified amountof frequency shifting (hereinafter referred to as shift amount) toimplement specific functions/applications, such as the key shifting orthe pitch shifting of the speech and music signals, or the frequencylowering of an audio signal or part of the frequency bands thereof toincrease the audibility or speech intelligibility. The concept of thefrequency shifting can be illustrated by a typical input-outputfrequency mapping characteristic in FIG. 1 (hereinafter referred to asfrequency shifting characteristic and abbreviated as FSC; in FIG. 1 ,½f_(SAM) denotes one half of the sampling rate of the audio input signalf_(SAM), which is the highest frequency of the digitized audio andreferred to as Nyquist frequency). If a frequency shifting system shiftseach frequency component of the audio input signal by a shift amount inproportion to the center frequency of the frequency component, thesystem possesses a linear FSC. Conventional speech/music pitch shiftingor vocoder operations belong to this category. If a frequency shiftingsystem shifts each frequency component of the audio input signal by ashift amount non-proportionally with the center frequency of thefrequency component, the system possesses a non-linear type FSC. Suchdesign is widely applied in hearing aids or hearing assistive devices.Because most hearing-impaired listeners suffer from high-frequencyhearing loss, the frequency shifting with a non-linear type FSC may helppart of the hearing-impaired listeners perceiving the high-frequencyinformation without changing the pitch of the speech signal. However,due to the destruction on the harmonicity relationship of the soundcomponents, the frequency shifting with a non-linear type FSC is notpreferable for music processing. In addition, to support different typesof applications, more flexibility on the FSC should be considered, forexample, it can be set as a many-to-one mapping characteristic (i.e., anon-monotonic characteristic suitable for a listener with a narrowaudible frequency range), one-to-many mapping characteristic (i.e.,shifting multiple replicas of a frequency component to differentfrequencies), or can be even dynamically changed depending on the typeof the audio input, these belongs to the design variants with modifiedFSCs.

To date, there are a variety of well-known frequency shifting algorithmsthat support the aforementioned FSCs, such as: performing frequencytransposition in a frequency range on a time-domain audio waveform(refer to Reference 1), adjusting an audio waveform by performing thesynchronized overlap-add (SOLA) method or its variants followed with aresampling operation (refer to Reference 2), transforming an audiowaveform to spectrums and performing the phase vocoder algorithm or itsvariants (refer to Reference 3), and performing frequency-divisionfiltering (i.e., performing multiple filter processing different incenter frequency to separate the audio components of differentfrequencies) on an audio waveform for the Rollers frequency shiftingalgorithm (refer to Reference 4) and so on. These algorithms aredifferent in multiple aspects. They are suitable for different signalprocessing architectures (e.g. time-domain processing orfrequency-domain processing). Each of them introduces different types ofartifacts. Each of them faces different restrictions, such as theapplicability of on-line and off-line applications, the applicability ofprocessing monophonic and polyphonic audio, the FSC type support (e.g.linear FSC, non-linear type FSCs, etc.). Moreover, they are with largevariation in computational complexity. To provide an audio output withhigh quality, natural sounding, minimized artifacts, and very lowprocessing delay in a real-time audio processing system, the Rollersfrequency shifting algorithm best fits these requirements. Theimplementation of the Rollers frequency-shifting algorithm is based on afilter bank design. In short, the filter bank is composed of multipleparalleled filters respectively corresponding to multiple frequencybands called sub-bands. Therefore, the paralleled filters are referredto as sub-band filters, and the output signal of each sub-band filter isreferred to as a sub-band signal.

The Rollers frequency shifting algorithm can be illustrated by the blockdiagram of FIG. 2 . A Rollers frequency shifting system 200 comprises alarge infinite impulse response (hereinafter abbreviated as IIR) filterbank 201, multiple paralleled real-to-complex converters and frequencyshifters 202, and a summation device 203. The filter bank 201 includes alarge number of sub-band filters (the number of filters suggested in theliterature is about hundreds to thousands), and each sub-band filter isimplemented by a fourth-order Butterworth filter to reduce thecomputational complexity of the frequency-division filtering. The IIRfilter bank 201 passes a real-type audio input signal through thesub-band filters to generate multiple real-type sub-band signalsrespectively (*1). The real-to-complex converters and the frequencyshifters 202 pass the real-type sub-band signals throughsingle-side-band modulation (which is an approximate function of theHilbert transform) so as to convert the sub-band signals to complex typesignals. After that, the frequency shifting operation of eachcomplex-type sub-band signal is performed according to the specifiedshift amount (determined by substituting the center frequency of thecorresponding sub-band into the FSC) to obtain one of a plurality ofshifted sub-band signals. Finally, the summation device 203 combines theshifted sub-band signals into an audio output signal. Since the audiooutput signal is of real type, the summation is performed only on thereal part values of the shifted sub-band signals. The Rollers frequencyshifting system 200 based on the filter bank is suitable forsample-based signal processing, and the processing delay of the systemis mainly contributed by the group delay of each sub-band filter of thefilter bank. It is usually significantly lower than the processing delayof the frequency-domain signal processing (*2), hence it is suitable forthe system design with low processing delay requirement. In addition,the main body of this architecture includes a large number of paralleledIIR filtering, single-side band conversion, and frequency shiftingoperations. These operations are highly parallelized (i.e., operationsof the respective sub-bands have no dependency on each other), which aresuitable for hardware implementation or execution on a multi-processorplatform.

(*1): If the sub-band filters of a filter bank share the same inputsignal, the filter bank is referred to as an analysis filter bank. TheIIR filter bank 201 is an analysis filter bank.

(*2): Frequency-domain signal processing is a frame-based processing.Because it is accompanied by a time-to-frequency transform and itsinverse transform, the algorithmic delay of the signal processing (aprocessing delay under zero arithmetic computation delay assumption,which is the theoretical minimum processing delay) is basically not lessthan one frame interval. However, the frame length has to be set longenough to make the frequency resolution of the spectrum meet therequirements of subsequent signal processing operations. Therefore, thefrequency resolution and delay requirements are a dilemma in real-timeaudio processing systems.Though with good output sound quality, low processing delay, simple andhighly parallelized architecture, the feasibility of implementing theRollers frequency shifting architecture on low-power mobile devices,wearable devices, and the real-time software platforms is still limiteddue to the large number of the high-order filtering and the singlesideband conversion operations (according to the literature, it is moresuitable to implement on a personal computer). Therefore, seeking afilter bank design suitable for supporting the frequency shiftingoperation while with low computational complexity is the key ofimplementing the time-domain frequency shifting algorithms for real-timeapplications on low-power wearable devices, mobile devices, or even onsoftware platforms.

REFERENCES DOCUMENTS

-   Reference 1: Dillon, H. Hearing aids, Sydney. Australia: Boomerang    Press, 2012.-   Reference 2: Dorran, David. “Audio time-scale modification.” Dublin    Institute of Technology Doctoral Thesis (2005).-   Reference 3: Laroche, Jean, and Mark Dolson. “New phase-vocoder    techniques for pitch-shifting, harmonizing and other exotic    effects.” Proceedings of the 1999 IEEE Workshop on Applications of    Signal Processing to Audio and Acoustics. WASPAA′99 (Cat. No.    99TH8452). IEEE, 1999.-   Reference 4: Juillerat, Nicolas, Simon Schubiger-Banz, and Stefan    Muller Arisona. “Low latency audio pitch shifting in the time    domain.” 2008 International Conference on Audio, Language and Image    Processing. IEEE, 2008.-   Reference 5: Dutoit, Thierry, and Ferran Marques. Applied Signal    Processing: A MATLAB™-based proof of concept. Springer Science &    Business Media, 2010.

SUMMARY

In view of the aforementioned key issues in these frequency shiftingsystems, the purpose of the present invention is to provide two audiofrequency shifting systems and corresponding two audio frequencyshifting procedures for real-time applications, and an analysis filterbank and a filter bank computing procedure applied in the audiofrequency shifting systems and the audio frequency shifting proceduresrespectively. The audio frequency shifting systems and the correspondingaudio frequency shifting procedures employ the analysis filter bank andthe filter bank computing procedures respectively to generate finespectrums used for dynamically estimating the corresponding shift amountof each sub-band signal. It reduces the overall computational complexityof the audio frequency shifting systems while maintains the audioquality, hence it is suitable for a real-time audio processing softwareimplementation and a low-power audio device implementation.

A first aspect of the present invention provides an analysis filter bankcorresponding to a plurality of sub-bands, comprising:

-   -   a plurality of sub-filters with different center frequencies        which perform a plurality of complex-type first-order IIR        filtering operations on an input signal to generate a plurality        of sub-filter signals;    -   a first set of binomial combiners, each of which performs a        weighted-sum operation on a first number of the sub-filter        signals with a first set of binomial weights to generate one of        a plurality of sub-band signals, wherein the first number of the        sub-filter signals are generated by the first number of the        sub-filters adjacent in center frequency;    -   a second set of binomial combiners, each of which performs a        weighted-sum operation on a second number of the sub-filter        signals with a second set of binomial weights to generate one of        a plurality of lower sub-band-edge signals or one of a plurality        of higher sub-band-edge signals, wherein the second number of        the sub-filter signals are generated by the second number of the        sub-filters adjacent in center frequency; and    -   a plurality of envelope detection with decimation devices which        perform a plurality of envelope detection with decimation        operations on the sub-band signals, the lower sub-band-edge        signals, and the higher sub-band-edge signals to generate a        plurality of fine spectrums.

A second aspect of the present invention provides an audio frequencyshifting system, comprising:

-   -   an analysis filter bank according to the first aspect, which        performs frequency-division filtering and envelope detection on        an input signal to generate a plurality of sub-band signals and        a plurality of fine input spectrums;    -   a frequency shifting controller, which estimates a plurality of        sub-band signal frequencies respectively corresponding to the        sub-band signals according to each of the fine input spectrums,        and determines a plurality of frequency shifting parameter sets        (hereinafter abbreviated as FSPSs) respectively corresponding to        a plurality of shifted sub-band signals according to the        sub-band signal frequencies;    -   a plurality of frequency shifting and weighting devices, each of        which corresponding to one of the FSPSs performs a frequency        shifting operation on one of the sub-band signals corresponding        to a sub-band number of the FSPS by a shift amount of the FSPS,        and weights a result of the frequency shifting operation by a        shifted sub-band weight of the FSPS to generate one of the        shifted sub-band signals; and    -   a sub-band combiner, which performs a sub-band combining        operation on the shifted sub-band signals to generate an output        signal.

A third aspect of the present invention provides an audio frequencyshifting system, comprising:

-   -   a framing and time-to-frequency transform device, which divides        an input signal into a plurality of audio frames with equal        frame length and equal frame spacing, and performs a        time-to-frequency transform on each of the audio frames to        generate a plurality of band signals;    -   a plurality of analysis filter banks according to the first        aspect, wherein the analysis filter banks respectively perform        frequency-division filtering and envelope detection on the band        signals to generate a plurality of sub-band signals and a        plurality of band spectrums, and the band spectrums at a frame        period are lumped as a fine input spectrum;    -   a frequency shifting controller, which estimates a plurality of        sub-band signal frequencies respectively corresponding to the        sub-band signals according to the fine input spectrum, and        determines a plurality of FSPSs corresponding to a plurality of        shifted sub-band signals according to the sub-band signal        frequencies;    -   a plurality of frequency shifting and weighting devices, each of        which corresponding to one of the FSPSs performs a frequency        shifting operation on one of the sub-band signals corresponding        to a sub-band number of the FSPS by a frequency shift amount of        the FSPS, and weights a result of the frequency shifting        operation by a shifted sub-band weight of the FSPS to generate        one of the shifted sub-band signals;    -   a plurality of sub-band combiners, each of which performs a        sub-band combining operation on a subset of the shifted sub-band        signals corresponding to a shifted band number to generate one        of a plurality of modified band signals; and    -   a frequency-to-time transform device, which performs a        frequency-to-time transform on a plurality of instantaneous        samples of the modified band signals at each frame period to        generate an output signal.

A fourth aspect of the present invention provides a filter bankcomputing procedure corresponding to a plurality of sub-bands,comprising the following steps:

-   -   performing a plurality of complex-type first-order IIR filtering        operations with different center frequencies on an input signal        to obtain a plurality of sub-filtered signals;    -   selecting a plurality of first subsets of the sub-filtered        signals, wherein each of the first subsets corresponding to one        of the sub-bands contains a first number of the sub-filtered        signals obtained from the first number of the filtering        operations adjacent in center frequency, and for each of the        first subsets, performing a weighted-sum operation on a        plurality of instantaneous values of the first number of the        sub-filtered signals in the subset at each sample period with a        first set of binomial weights to obtain one of a plurality of        sub-band signals;    -   selecting a plurality of second subsets of the sub-filtered        signals, wherein each of the second subsets corresponding to a        lower-frequency side or a higher-frequency side of one of the        sub-bands contains a second number of the sub-filtered signals        obtained by the second number of the filtering operations        adjacent in center frequency, and for each of the second        subsets, performing a weighted-sum operation on a plurality of        instantaneous values of the second number of the sub-filtered        signals in the subset at each sample period with a second set of        binomial weights to obtain one of a plurality of lower        sub-band-edge signals or one of a plurality of higher        sub-band-edge signals; and    -   performing a plurality of envelope detection with decimation        operations on the sub-band signals, the lower sub-band-edge        signals, and the higher sub-band-edge signals to obtain at least        one fine spectrum.

A fifth aspect of the present invention provides an audio frequencyshifting procedure, comprising the following steps:

-   -   executing a filter bank computing procedure according to the        fourth aspect on an input signal to obtain a plurality of        sub-band signals and at least one fine input spectrum;    -   estimating a plurality of sub-band signal frequencies        respectively corresponding to the sub-band signals according to        each of the at least one fine input spectrum, and determine a        plurality of FSPSs corresponding to a plurality of shifted        sub-band signals according to the sub-band signal frequencies;    -   for each of the FSPSs, performing a frequency shifting operation        on one of the sub-band signals corresponding to a sub-band        number of the FSPS by a shift amount of the FSPS, and        multiplying a result of the frequency shifting operation by a        shifted sub-band weight of the FSPS to obtain one of the shifted        sub-band signals; and    -   performing a sub-band combining operation on the shifted        sub-band signals to obtain an output signal.

The sixth aspect of the present invention provides an audio frequencyshifting procedure, comprising the following steps:

-   -   performing a time-to-frequency transform operation on at least        one frame of an input signal to obtain a plurality of band        signals;    -   executing a plurality of filter bank computing procedures        according to the fourth aspect on the band signals to obtain a        plurality of sub-band signals and a plurality of band spectrums,        and lumping the band spectrums at each frame period as a fine        input spectrum;    -   estimating a plurality of sub-band signal frequencies        respectively corresponding to the sub-band signals according to        the fine input spectrum, and determining a plurality of FSPSs        respectively corresponding to a plurality of shifted sub-band        signals according to the sub-band signal frequencies;    -   for each of the FSPSs, performing a frequency shifting operation        on one of the sub-band signals corresponding to a sub-band        number of the FSPS by a shift amount of the FSPS, and        multiplying a result of the frequency shifting operation by a        shifted sub-band weight of the FSPS to obtain one of the shifted        sub-band signals;    -   for each of a plurality of shifted band numbers appearing in the        FSPSs, performing a sub-band combining operation on a subset of        the shifted sub-band signals corresponding to the shifted band        number to obtain one of a plurality of modified band signals;        and    -   performing a frequency-to-time transform operation on a        plurality of instantaneous samples of the modified band signals        at each frame period to obtain an output signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot of a static input-output frequency mappingcharacteristic.

FIG. 2 is a block diagram of a Rollers frequency shifting system basedon a filter bank.

FIG. 3 is a block diagram of an analysis filter bank of the presentinvention.

FIG. 4 is a flow chart of a filter bank computing procedure of thepresent invention.

FIG. 5 is a block diagram of an audio frequency shifting system of afirst embodiment of the present invention.

FIG. 6 is a response plot of an analysis filter bank of the presentinvention with equal-width sub-bands and employing first-order binomialcombiners.

FIG. 7 is a response plot of an analysis filter bank of the presentinvention employing second-order binomial combiners.

FIG. 8 is a response plot of the analysis filter bank of the presentinvention employing second-order binomial combiners with responsecompensation.

FIG. 9 is a flowchart of an audio frequency shifting procedure of asecond embodiment of the present invention.

FIG. 10 is a block diagram of a hybrid audio frequency shifting systemof a third embodiment of the present invention.

FIG. 11 is a flowchart of a hybrid audio frequency shifting procedure ofa fourth embodiment of the present invention.

DETAILED DESCRIPTION

To make the present invention better understood by those skilled in theart to which the present invention pertains, preferred embodiments ofthe present invention are detailed below with the accompanying drawingsto clarify the content of the present invention and effects to beachieved thereof.

FIG. 3 is a block diagram of an analysis filter bank of the presentinvention. The four embodiments of the present invention all comprisethe analysis filter bank or its functionally equivalent computingprocedure. The analysis filter bank 300 corresponds to S sub-bandsnumbered from low to high according to the sub-band center frequencies.The analysis filter bank 300 comprises multiple paralleled first-orderIIR sub-filters 301, a first set of paralleled combiners based on a setof M^(th)-order binomial weights (hereinafter referred to asM^(th)-order binomial combiners; M≥1) 302, a second set of paralleledcombiners based on a set of {circumflex over (M)}^(th)-order binomialweights (hereinafter referred to as {circumflex over (M)}^(th)-orderbinomial combiners; {circumflex over (M)}≥1) 303, and multipleparalleled envelope detection with decimation devices 304. The first setof M^(th)-order binomial combiners 302 combine the output signals of thefirst-order IIR sub-filters 301 (hereinafter referred to as sub-filtersignals) to generate multiple sub-band signals. Considering that thesub-band signals can be obtained by passing an audio input signal of theanalysis filter bank through multiple independent filters respectivelycorresponding to the sub-bands, such independent filters are hereinafterreferred to as equivalent sub-band filters.

The paralleled first-order IIR sub-filters 301 are with different centerfrequencies and are numbered according to their center frequencies fromlow to high. Each IIR sub-filter performs a complex-type first-order IIRfiltering operation on an audio input signal to generate one of aplurality of sub-filter signals. The IIR filtering operation can beexpressed as:y _(IIR,k)[n]=b _(k) ·x[n]−α_(k) ·y _(IIR,k)[n−1],  (1)wherein k denotes the No. of the IIR sub-filter, n denotes the samplingtime index, x denotes the audio input signal, and y_(IIR,k) denotes theNo. k sub-filter signal, a_(k) and b_(k) denote a complex-type feedbackcoefficient and a real-type feed-forward coefficient of the No. k IIRsub-filter respectively, expressed as:

$\begin{matrix}{{a_{k} = {\left( {1 - \frac{BW_{{IIR},k}}{f_{SAM}}} \right) \cdot {\exp\left\lbrack {j\left( {2{\pi \cdot \frac{f_{{IIR},k}}{f_{SAM}}}} \right)} \right\rbrack}}},} & (2)\end{matrix}$ $\begin{matrix}{{b_{k} = {\rho \cdot \left( \frac{BW_{{IIR},k}}{f_{SAM}} \right)^{\mu}}},} & (3)\end{matrix}$wherein f_(IIR,k) and BW_(IIR,k) denote the center frequency and thebandwidth (*) of the No. k IIR sub-filter respectively, f_(SAM) denotesthe sampling rate of the audio input signal of the analysis filter bank300, μ and ρ denote the two parameters of the IIR sub-filters 301.Changing μ may alter the averaged passband level of the IIR sub-filterresponse, and changing ρ may alter the variation of the passband levelsof the IIR sub-filter responses over sub-bands. The goal of adjusting μand ρ is to make the passband gain response of each sub-band close to 0dB.*: The bandwidth of each of the IIR sub-filters 301 is determined by thewidth of at least one corresponding sub-band. For example, in a filterbank design with equal-width sub-bands, the bandwidths of the IIRsub-filters 301 are identical. In a design where the sub-band widthincreases with the sub-band center frequency, the bandwidth of each ofthe IIR sub-filters 301 increases with the sub-filter center frequency.

Each of the first set of M^(th)-order (M≥1) binomial combiners 302performs a weighted-sum operation on M+1 of the sub-filtered signalswith a set of M^(th)-order binomial weights to generate one of thesub-band signals, wherein the M+1 of the sub-filter signals aregenerated by the M+1 of the IIR sub-filters 301 adjacent in centerfrequency (i.e., consecutively numbered). The m^(th) weight of the setof M^(th)-order binomial weights is the m^(th) coefficient of thepolynomial expansion of (1−x)^(M):

$\begin{matrix}{{B_{M,m} = {\left( {- 1} \right)^{m} \cdot \frac{M!}{{m!}{\left( {M - m} \right)!}}}},} & (4)\end{matrix}$and the weighted-sum operation of the first set of M^(th)-order binomialcombiners 302 can be expressed as:

$\begin{matrix}{{{y_{{FB},s}\lbrack n\rbrack} = {\sum\limits_{m = 0}^{M}{B_{M,m} \cdot {y_{{IIR},{k_{s} + m}}\lbrack n\rbrack}}}},{\forall{s \in \left\lbrack {1,S} \right\rbrack}}} & (5)\end{matrix}$where s denotes the No. of the combiner (equal to the No. of thecorresponding sub-band), y_(FB,s) denotes the No. s sub-band signal ofthe analysis filter bank 300, and k_(s) denotes the lowest No. of thesub-filter signals used by the No. s combiner of the first set ofM^(th)-order binomial combiners 302, y_(IIR,k) _(s) _(+m) denotes theNo. k_(s)+m sub-filter signal, and the remaining notations are asaforementioned. Considering that two sub-band signals respectivelycorresponding to any two of the sub-bands adjacent in frequency share Psub-filter signals (i.e., two of the first set of M^(th)-order binomialcombiners 302 with any two consecutive No. share P sub-filters signal,where P∈[0, M]), then k_(s) can be expressed as:k _(s)=(M−P+1)·(s−1)+1.  (6)Therefore, the first set of M^(th)-order binomial combiners 302corresponds to (M−P+1)·S+P IIR sub-filters in total.

The reason of employing higher-order binomial combiners is to increasethe stopband attenuation level and the transition-band attenuationslopes of the frequency responses of the equivalent sub-band filters.The stopband attenuation levels of the filter responses of thefirst-order IIR sub-filters are about 20 to 30 dB. Through theweighted-sum operations with the M^(th)-order binomial weights, thestopband attenuation levels and the transition-band attenuation slopesof the frequency response of the equivalent sub-band filtercorresponding to each sub-band can be increased by multiples. While thedrawback is that the group delays of the equivalent sub-band filter arealso increased by multiples. Hence the applicability of employinghigher-order binomial combiners has to be considered in conjunction withthe system applications.

Each of the second set of {circumflex over (M)}^(th)-order ({circumflexover (M)}≥1) binomial combiners 303 performs a weighted-sum operation on{circumflex over (M)}+1 of the sub-filtered signals by a set of{circumflex over (M)}^(th)-order binomial weights to generate one of thelower sub-band-edge signals or one of the higher sub-band-edge signals,wherein the {circumflex over (M)}+1 of the sub-filter signals aregenerated by the {circumflex over (M)}+1 of the IIR sub-filters 301adjacent in center frequency (i.e., consecutive numbers). This set of{circumflex over (M)}^(th)-order binomial weights can be generated bysubstituting {circumflex over (M)} into M of equation (4). Theoperations of the second set of {circumflex over (M)}^(th)-orderbinomial combiners 303 can be expressed as:

$\begin{matrix}\left\{ {\begin{matrix}{{y_{{LE},s}\lbrack n\rbrack} = {\sum\limits_{m = 0}^{\hat{M}}{B_{\hat{M},m} \cdot {y_{{IIR},{k_{s} - \delta_{LE} + m}}\lbrack n\rbrack}}}} \\{{y_{{UE},s}\lbrack n\rbrack} = {\sum\limits_{m = 0}^{\hat{M}}{B_{\hat{M},m} \cdot {y_{{IIR},{k_{s} + \delta_{UE} + m}}\lbrack n\rbrack}}}}\end{matrix},{\forall{s \in \left\lbrack {1,S} \right\rbrack}}} \right. & (7)\end{matrix}$wherein y_(LE,s) denotes the lower sub-band-edge signal corresponding toNo. s sub-band, y_(UE,s) denotes the higher sub-band-edge signalcorresponding to No. s sub-band, and δ_(LE,s) and δ_(UE,s) denote anegative index offset and a positive index offset for deriving y_(LE,s)and y_(UE,s) respectively, y_(IIR,k) _(s) _(−δ) _(LE) _(+m) denotes theNo. k_(s)−δ_(LE)+m sub-filter signal, y_(IIR,k) _(s) _(+δ) _(UE) _(+m)denotes the No. k_(s)+δ_(UE)+m sub-filter signal,B_({circumflex over (M)},m) denotes the m^(th) weight of the set of{circumflex over (M)}^(th)-order binomial weights, and the remainingnotations are as aforementioned.

In addition, the settings of the two index offsets δ_(LE), δ_(UE)satisfy:

$\begin{matrix}\left\{ {\begin{matrix}{\delta_{LE} \in \left\lbrack {0,{M - P + 1}} \right\rbrack} \\{\delta_{UE} = {\delta_{LE} + M - \hat{M}}}\end{matrix},} \right. & (8)\end{matrix}$where the notations are as aforementioned. Under the restriction of (8),the weighted-sum operations of y_(LE,s) and y_(FB,s) share at least oneof the sub-filter signals, and the combining operations of y_(UE,s) andy_(FB,s) also share at least one of the sub-filter signals. The centerfrequency of the No. s higher sub-band-edge signal is located betweenthe center frequency of the No. s sub-band and the center frequency ofthe No. s+1 sub-band (such a frequency range is also referred to as ahigher-frequency side of the No. s sub-band), and the center frequencyof the No. s lower sub-band-edge signal is located between the centerfrequency of the No. s sub-band and the center frequency of the No. s−1sub-band (such a frequency range is also referred to as alower-frequency side of the No. s sub-band). Therefore, the second setof {circumflex over (M)}^(th)-order binomial combiners 303 correspondsto (M−P+1)·S+P+2·δ_(LE) IIR sub-filters in total.

Normally, the number of combiners of the second set of {circumflex over(M)}^(th)-order binomial combiners 303 (generating the lowersub-band-edge signals and the higher sub-band-edge signals) is twice thenumber of combiners of the first set of M^(th)-order binomial combiners302 (generating the sub-band signals). While the number of combiners canbe further reduced if the settings of {circumflex over (M)} and δ_(LE)satisfy the following relationship:

$\begin{matrix}\left\{ {\begin{matrix}{\hat{M} \in \left\lbrack {{P + 1},{{2M} - P + 1}} \right\rbrack} \\{\delta_{LE} = {\left( {\hat{M} + 1 - P} \right)/2}}\end{matrix}.} \right. & (9)\end{matrix}$According to (7)˜(9), we have y_(UE,s)[n]=y_(LE,s+1)[n] ∀n, i.e., theNo. s higher sub-band-edge signal and the No. s+1 lower sub-band-edgesignal are identical. The constraint of (9) reduces the number ofcombiners of the second set of {circumflex over (M)}^(th)-order binomialcombiners 303 to S+2. Therefore, the extra computations of the analysisfilter bank 300 to support the frequency shifting can be reduced.

The envelope detection with decimation devices 304 performs multipleenvelope detection with decimation operations on the sub-band signals,the lower sub-band-edge signals, and the higher sub-band-edge signals togenerate multiple fine spectrums (a decimation operation is just aninteger down-sampling, where the down-sampling ratio, also referred toas decimating factor, is a ratio of the sampling rate of the audio inputsignal over the frame rate of the fine spectrum). Generally speaking,the envelope of a signal can be generated by detecting the amplitude,power, power level or related information of the signal and smoothingthe detection result in the time domain and/or the frequency domain.Taking the detection of the amplitude envelope as an example, theenvelope detection with decimation devices 304 passes the amplitudevalues of the sub-band signals, the amplitude values of the lowersub-band-edge signals, and the amplitude values of the highersub-band-edge signals to a leaky integration stage to generate multipleamplitude envelopes, and decimates the amplitude envelopes by adecimating factor of greater than one to form the fine spectrums with alower frame rate (the sampling period of the decimated envelopes, whichis the reciprocal of the frame rate, is referred to as the decimationperiod). The envelope detection operations can be expressed as:

$\begin{matrix}\left\{ {\begin{matrix}{{u_{L,s}\lbrack n\rbrack} = {{\left( {1 - \alpha} \right) \cdot {u_{L,s}\left\lbrack {n - 1} \right\rbrack}} + {\alpha \cdot {❘{y_{{LE},s}\lbrack n\rbrack}❘}}}} \\{{u_{C,s}\lbrack n\rbrack} = {{\left( {1 - \alpha} \right) \cdot {u_{C,s}\left\lbrack {n - 1} \right\rbrack}} + {\alpha \cdot {❘{y_{{FB},s}\lbrack n\rbrack}❘}}}} \\{{u_{U,s}\lbrack n\rbrack} = {{\left( {1 - \alpha} \right) \cdot {u_{U,s}\left\lbrack {n - 1} \right\rbrack}} + {\alpha \cdot {❘{y_{{UE},s}\lbrack n\rbrack}❘}}}}\end{matrix},{\forall{s \in \left\lbrack {1,S} \right\rbrack}}} \right. & (10)\end{matrix}$wherein u_(L,s), u_(U,s), u_(C,s) denote the amplitude envelope of theNo. s lower sub-band-edge signal, the amplitude envelope of the No. shigher sub-band-edge signal, and the amplitude envelope of the No. ssub-band signal respectively, a denotes the leaky factor of the leakyintegration, and the remaining notations are as aforementioned. Toensure that the reduction of the frame rate of the fine spectrum throughdecimation does not affect the audio quality of the subsequent frequencyshifting result, the frame rate of the fine spectrum should not be lessthan twice the bandwidth of the widest sub-band (to fulfill the samplingtheorem). Each of the fine spectrums includes a plurality ofinstantaneous values of the amplitude envelopes of the sub-band signals,the amplitude envelopes of the lower sub-band-edge signals, and theamplitude envelopes of the higher sub-band-edge signals at a decimationperiod. Such fine spectrum information with frequency resolution higherthan that of the sub-band signals facilitates the frequency shiftingcontroller 501 determining the corresponding shift amount of eachsub-band.

In addition to being implemented by a physical device, the function ofthe analysis filter bank 300 can also be implemented by an equivalentcomputing procedure executed on at least one processor. FIG. 4 is theflowchart of a filter-bank computing procedure of the present invention.The filter-bank computing procedure corresponds to multiple sub-bands.In describing the steps of the filter-bank computing procedure,equations (1) to (10) and the corresponding paragraphs are referred. Theflow steps focus on the processing method of a segment of a continuousaudio signal, because the signal is segmentally processed for each stepto support a real-time audio application, i.e., each step processes anoutput signal segment just obtained by the previous step instead ofwaiting the entire output signal obtained by the previous step.

In FIG. 4 , a plurality of complex-type first-order IIR filteringoperations with different center frequencies are performed on at leastone sample of an audio input signal to obtain a plurality ofsub-filtered signals respectively (step S101). Referring to paragraph[0015], the complex-type first-order IIR filtering operationscorresponds to the calculation of equation (1) to (3). Each sub-filteredsignal includes at least one sample.

A plurality of first subsets of the sub-filtered signals are selected,wherein each of the first subsets corresponding to one of the sub-bandscontains a first number (≥2) of the sub-filtered signals obtained by thefirst number of the filtering operations adjacent in center frequency.For each of the first subsets, a weighted-sum operation is performed ona plurality of instantaneous values of the first number of thesub-filtered signals in the subset at each sample period with a firstset of binomial weights to obtain one of a plurality of sub-band signals(step S102). Referring to paragraphs [0016] and [0017], the weighted-sumoperation based on the first set of binomial weights corresponds to thecalculation of equation (5). Each sub-band signal includes at least onesample.

A plurality of second subsets of the sub-filtered signals are selected,wherein each of the second subsets corresponding to a lower-frequencyside or a higher-frequency side of one of the sub-bands contains asecond number (≥2) of the sub-filtered signals obtained by the secondnumber of the filtering operations adjacent in center frequency. Foreach of the second subsets, a weighted-sum operation is performed on aplurality of instantaneous values of the second number of thesub-filtered signals in the subset at each sample period with a secondset of binomial weights to obtain one of a plurality of lowersub-band-edge signals or one of a plurality of higher sub-band-edgesignals (step S103). Referring to paragraphs [0018] to [0020], theweighted-sum operation based on the second set of binomial weightscorresponds to equation (7). Each of the lower sub-band-edge signals andthe higher sub-band-edge signals includes at least one sample

A plurality of envelope detection with decimation operations areperformed on the sub-band signals, the lower sub-band-edge signals, andthe higher sub-band-edge signals to obtain at least one fine spectrum(step S104), wherein each fine spectrum includes a plurality ofinstantaneous values of the envelopes of the sub-band signals, theenvelopes of the lower sub-band-edge signals, and the envelopes of thehigher sub-band-edge signals at a decimation period. Refer to equation(10) and paragraph [0021] for more detail of the envelope detection withdecimation operations.

FIG. 5 is a block diagram of an audio frequency shifting system of thefirst embodiment of the present invention. The audio frequency shiftingsystem 500 comprises an analysis filter bank 300, a frequency shiftingcontroller 501, a plurality of frequency shifting and weighting devices502, and a sub-band combiner 503.

The analysis filter bank 300 performs frequency-division filtering andenvelope detection on an audio input signal according to a plurality ofsub-bands to generate multiple sub-band signals and multiple fine inputspectrums. The audio input signal is a digitized waveform, which maycome from the output of an analog-to-digital converter, from an audiostorage device, or further down sampling the signal (while the soundover the listener's audible frequency range is preserved) before beinginputted to the audio frequency shifting system 500. Down sampling savesunnecessary computations on processing the high-frequency soundinaudible by the listener. In addition, it may prevent thehigh-frequency sound from occupying the limited dynamic range ofnumerical operations.

The frequency shifting controller 501 determines multiple frequencyshift amounts and multiple shifted sub-band weights of the sub-bandsignals according to each of the fine input spectrums. Morespecifically, the frequency shifting controller 501 estimates aplurality of sub-band signal frequencies respectively corresponding tothe sub-band signals according to each of the fine input spectrums,which can be expressed as:

$\begin{matrix}{{{{\overset{\sim}{f}}_{{SB},s}\lbrack h\rbrack} = {f_{{SB},s} + {C_{{CFO},s} \cdot \frac{{u_{U,s}\lbrack h\rbrack} - {u_{L,s}\lbrack h\rbrack}}{{u_{U,s}\lbrack h\rbrack} + {u_{C,s}\lbrack h\rbrack} + {u_{L,s}\lbrack h\rbrack}}}}},{\forall{s \in \left\lbrack {1,S} \right\rbrack}}} & (11)\end{matrix}$wherein h denotes the time index of the fine input spectrum, {tilde over(f)}_(SB,s) denotes the No. s sub-band signal frequency (i.e., centerfrequency of the No. s sub-band signal), f_(SB,s) denotes the centerfrequency of the No. s sub-band, C_(CFO,s) denotes the scaling factor ofthe No. s sub-band, and the remaining notations are as aforementioned.To avoid excessive frequency estimation error, {tilde over (f)}_(SB,s)can be further limited between the lowest and highest center frequenciesof the IIR sub-filters corresponding to the No. s sub-band, i.e., {tildeover (f)}_(SB,s)∈[f_(IIR,k) _(s) , f_(IIR,k) _(s) _(+M)]. Moreover, theC_(CFO,s) settings are aimed to make the two sub-band signal frequenciesof equation (11) corresponding to any two adjacent sub-bands roughlyequal as a single-frequency input falls at the boundary of the twoadjacent sub-bands (i.e., if the audio input signal is a single tonewith a frequency at the boundary of the No. s and No. s+1 sub-bands, bycalculating (11) we have {tilde over (f)}_(SB,s)[h]≈{tilde over(f)}_(SB,s+1)[h]∀h). Such C_(CFO,s) setting is roughly proportional tothe width of the No. s sub-band. In case the analysis filter bank 300 iswith equal-width sub-bands, the settings of C_(CFO,s) for all sub-bandsare equal.

In addition to equation (11), alternative ways to estimate the frequencyof the spectrum components do exist. For instance, in Reference 3 anapproach based on the second-order polynomial fitting (also known aspolynomial regression) is proposed, which takes three consecutivesamples around a local peak on an audio spectrum to estimate the centerfrequency of each partial. The partial is a narrow-band component of theaudio signal, which corresponds to a spectral region including the localpeak on the audio spectrum.

After estimating the sub-band signal frequencies, the frequency shiftingcontroller 501 substitutes each sub-band signal frequency into a FSCwhich allows one-to-many mapping. Specifically, each sub-band signal isdesignated to be mapped to at least one shifted sub-band signal, whereeach shifted sub-band signal is characterized by a shift amount (thedifference between the center frequencies of the shifted sub-band signaland the corresponding sub-band signal) and a shifted sub-band weight(the ratio of the shifted sub-band signal strength over thecorresponding sub-band signal strength). After subsequent frequencyshifting operations, a total of Ŝ shifted sub-band signals are generatedfrom S sub-band signals (Ŝ≥S), where the No. s sub-band signal isfrequency shifted to generate the No. Ŝ_(s-1)+1 to Ŝ_(s) shiftedsub-band signals (Ŝ₀=0, Ŝ_(s)≥Ŝ_(s-1)+1, and Ŝ_(s)=Ŝ). In a nutshell,the frequency shifting controller 501 determines Ŝ FSPSs respectivelycorresponding to the Ŝ shifted sub-band signals according to the Ssub-band signal frequencies, where each of the FSPSs includes a sub-bandnumber, a shift amount, and a shifted sub-band weight.

In practice, the shift amount of a FSC is zero in part of the sub-bands(it is common for non-linear type FSCs). In this case, there is no needto estimate the corresponding sub-band signal frequencies, nor tocalculate the corresponding lower sub-band-edge signal, highersub-band-edge signal, and their envelopes.

Each of the frequency shifting and weighting devices 502 correspondingto one of the FSPSs performs a frequency shifting operation on one ofthe sub-band signals corresponding to a sub-band number of the FSPS by ashift amount of the FSPS, and weights a result of the frequency shiftingoperation by a shifted sub-band weight of the FSPS to generate one ofthe shifted sub-band signals. The frequency shifting operation and theweighting operation can be expressed as:

$\begin{matrix}{{{y_{{SHF},v}\lbrack n\rbrack} = {{real}\left\{ {{y_{{FB},s}\lbrack n\rbrack} \cdot {w_{v}\lbrack n\rbrack} \cdot {\exp\left\lbrack {j \cdot \left( {\theta_{v} + {\frac{2\pi}{f_{SAM}}{\sum\limits_{t = 0}^{n}{f_{{SHF},v}\lbrack t\rbrack}}}} \right)} \right\rbrack}} \right\}}},{\forall{v \in \left\lbrack {{{\hat{S}}_{s - 1} + 1},{\hat{S}}_{s}} \right\rbrack}},{s \in \left\lbrack {1,S} \right\rbrack}} & (12)\end{matrix}$wherein y_(SHF,v) denotes the No. v shifted sub-band signal, which isobtained by performing aforementioned frequency shifting and weightingoperation on the No. s sub-band signal y_(FB,s), real(·) denotes afunction of taking the real part value of a complex value, w_(v) denotesthe shifted sub-band weight of the No. v shifted sub-band signal,f_(SHF,v) denotes the shift amount of the No. v shifted sub-band signal,f_(SAM) denotes the sampling rate of the audio input signal, θ_(v)denotes an initial phase of the No. v shifted sub-band signal, and theremaining notations are as aforementioned. To simplify therepresentation, the time indices of the frequency shift parameters suchas w_(v) and f_(SHF,v) are set the same as the time index of the shiftedsub-band signals. Actually, the FSPSs are generated at a rate equal toor lower than the frame rate of the fine input spectrum. When computingthe values of the shifted sub-band signals at each sample period, thelatest FSPSs corresponding to the sample period are adopted. Moreover,since the output of the audio frequency shifting system 500 is of realtype, only the real part values of the shifted sub-band signals arerequired for subsequent combining operations.

For each shifted sub-band signal with zero shift amount, the setting ofθ_(v) in equation (11) affects the frequency response of the outputsignal of the system. The present invention suggests to determine θ_(v)according to the center frequency of the No. s sub-band corresponding tothe No. v shifted sub-band signal regardless of the shift amountf_(SHF,v). For example, in the embodiment of the present invention, thesub-bands are numbered from low to high according to the sub-band centerfrequencies, hence θ_(v) is set to a value proportional to s where s isthe sub-band number corresponding to the No. v shifted sub-band signal(in the following examples, θ_(v) is set to −s·π/2).

The sub-band combiner 503 performs a sub-band combining operation on theshifted sub-band signals to generate an audio output signal, where thesub-band combining operation is based on the configuration of thefrequency shift sub-bands. Specifically, if the shifted sub-band signalsare of equal bandwidth, the sub-band combiner 503 sums a plurality ofinstantaneous samples of the shifted sub-band signals with zero shiftamount and with non-zero shift amounts at each sample period to generatea zero-shifting sub-band summation signal and a non-zero-shiftingsub-band summation signal respectively. Then, the sub-band combiner 503adds the zero-shifting sub-band summation signal underwent a linearfiltering operation and the non-zero shift sub-band summation signal togenerate the audio output signal, expressed as:

$\begin{matrix}\left\{ {\begin{matrix}{{y_{U}\lbrack n\rbrack} = {\sum\limits_{v \in V}{y_{{SHF},v}\lbrack n\rbrack}}} \\{{y_{v}\lbrack n\rbrack} = {\sum\limits_{v \in V}{y_{{SHF},v}\lbrack n\rbrack}}}\end{matrix},} \right. & (13)\end{matrix}$ $\begin{matrix}{{{y\lbrack n\rbrack} = {{y_{U}\lbrack n\rbrack} + {C_{CMP} \cdot {y_{U}\left\lbrack {n - D} \right\rbrack}} + {y_{v}\lbrack n\rbrack}}},{D = {{round}\left( \frac{f_{SAM}}{BW} \right)}}} & (14)\end{matrix}$wherein U denotes a set of No. of all shifted sub-band signals with zeroshift amount, V denotes a set of No. of all shifted sub-band signalswith non-zero shift amount, y_(U) denotes the zero-shifting sub-band sumsignal (i.e., sum of the shifted sub-band signals of set U), y_(V)denotes the non-zero-shifting sub-band sum signal (i.e., sum of theshifted sub-band signals of set V), y denotes an audio output signal ofthe audio frequency shifting system 500, BW denotes the bandwidth of theshifted sub-bands, C_(CMP) denotes an adjustable parameter, rounddenotes the rounding function, and the remaining notations are asaforementioned. The output audio may be output to a digital-to-analogconverter to generate an analog waveform, output to a storage device orother systems, or further up-sampled before being output.

The frequency responses (including gain responses and group delayresponses) of the equivalent sub-band filters of the analysis filterbank 300 are highly similar in shape near the passband when thesub-bands are of equal width. Through summation, the overall gainresponse and group delay response of the analysis filter bank 300exhibit periodic fluctuations, and the filtering operation of equation(14) is aimed to mitigate such effect. That is, adjusting the parameterC_(CMP) in (14) may reduce the fluctuations of the overall responses(only for the sub-band signals with zero shift amount).

If the bandwidths of the shifted sub-band signals are not equal, or most(or all) shift amounts of the shifted sub-band signals are non-zero, theoverall responses of the analysis filter bank 300 cannot be compensatedby the filtering operation of (14). Therefore, the sub-band combiner 503simply sums a plurality of instantaneous samples of the shifted sub-bandsignals at each sample period to generate the audio output signal,expressed as:

$\begin{matrix}{{{y\lbrack n\rbrack} = {\sum\limits_{v = 1}^{\hat{S}}{y_{{SHF},v}\lbrack n\rbrack}}},} & (15)\end{matrix}$where the notations are as aforementioned.

FIG. 6 is a response plot of an analysis filter bank of the presentinvention with equal-width sub-bands and employing first-order binomialcombiners, wherein the solid lines denote the equivalent sub-band filterresponses, and the dashed lines denote the equivalent filter responsescorresponding to the lower sub-band-edge signals or the highersub-band-edge signals, the dotted lines denote the overall responses ofthe analysis filter bank (i.e., the frequency responses obtained bycombining the outputs of the equivalent sub-band filters with zerofrequency shift amount. In a non-linear type FSC, the shift amount istypically zero in low frequency region, causing the frequency shiftingoperation behaves a linear filtering with said response inlow-frequency). In this example, the sampling rate of the audio inputsignal is 12 kHz, and the frequency region from zero frequency (DC) toNyquist frequency is divided into 18 sub-bands, so the width of eachsub-band is 333 Hz. The combiner configuration of the analysis filterbank 300 is set as M=1 and {circumflex over (M)}=2. Thus, the analysisfilter bank 300 requires 21 first-order IIR sub-filters, each sub-bandsignal is composed of two sub-filter signals, and the center frequenciesof the two corresponding IIR sub-filters with the same bandwidth arelocated at the boundaries between the sub-band and the adjacent twosub-bands. In addition, each of the lower sub-band-edge signals and thehigher sub-band-edge signals is composed of three sub-filtered signals,wherein the No. s higher sub-band-edge signal is the same as the No. s+1lower sub-band-edge signal.

FIG. 7 is a response plot of an analysis filter bank of the presentinvention employing second-order binomial combiners, where the samplingrate of the audio input signal, the number of sub-bands, and thesub-band width of the analysis filter bank are all equal to the settingsof the above example. The combiner configuration of the analysis filterbank 300 is M={circumflex over (M)}=2. Thus, the analysis filter bank300 requires 39 first-order IIR sub-filters, and each of the sub-bandsignals is composed of three of the sub-filter signals. The centerfrequencies of two of the three IIR sub-filters are located at theboundaries between the sub-band and the adjacent two sub-bands, and thecenter frequency of the remaining IIR sub-filter is located at thecenter of the sub-band. In addition, each of the lower sub-band-edgesignals and the higher sub-band-edge signal is composed of three of thesub-filtered signals, and the No. s higher sub-band-edge signal is thesame as the No. s+1 lower sub-band-edge signal. To make the figuresclear, fewer sub-bands are employed in the two examples. From the twoexamples it can be seen that the transition band of the gain response ofthe equivalent sub-band filters of the analysis filter bank employingthe second-order binomial combiner is narrower than that of the analysisfilter bank employing the first-order binomial combiner, while the stopband attenuation is stronger as well. The price for obtaining suchbetter response characteristic is that the number of complex-typemultiplications is almost doubled, and the filter group delay is alsodoubled.

FIG. 8 is a response plot of the analysis filter bank of the presentinvention employing second-order binomial combiners with responsecompensation, wherein the solid lines denote the equivalent sub-bandfilter responses, and the dashed lines denote the overall responses ofthe analysis filter bank. The configuration of the analysis filter bankis almost identical to that of the example shown in FIG. 7 except theenabled response compensation. It can be seen that through the simplefiltering operation of (14), the overall response is flatter than thatshown in FIG. 7 .

The following explains the known difference between the frequencyshifting system of the first embodiment and the aforementioned Rollersalgorithm:

-   -   Difference in the way of determining the shift amounts: In the        Rollers algorithm, the shift amount of each sub-band signal is        determined based on the center frequency of the corresponding        sub-band. An issue arising with this approach is that each        frequency component of the input signal may appear at the        outputs of multiple sub-band filters adjacent in center        frequency, where the shift amounts respectively corresponding to        the sub-band filters are different. Consequently, an obvious        low-frequency interference referred to as beat is introduced by        combining the shifted sub-band signals. A countermeasure to        mitigate the issue is to increase the number of sub-bands to        reduce the sub-band width. Through this, the frequency of the        beat will be reduced, the response overlapping of adjacent        sub-band filters will be decreased, and the intensity of        interference components will be reduced accordingly. However,        increasing the number of sub-bands directly increases the        computational complexity and the group delay of the filter bank.        Reducing the response overlapping of adjacent sub-band filters        causes a worse attenuation on signal near the sub-band edges,        which requires to increase the order of the sub-band filters to        alleviate such effect (with the cost of raising both the        computational complexity and the processing delay). Therefore,        the countermeasure are not generally preferred in system design.        By contrast, in the audio frequency shifting system 500, the        shift amount of each sub-band signal is determined according to        the fine input spectrum. Since the sub-band signal frequencies        of the two adjacent sub-bands are roughly equal when the        frequency of a sound component locates between the center        frequencies of the two sub-bands, this design reduces the        probability of beat introduced after combining the shifted        signals, and it also avoids the issues introduced by reducing        the sub-band width or reducing the response overlapping of        adjacent sub-band filters. Another unique feature of the design        of the first embodiment is that the highly shared IIR        sub-filters of the analysis filter bank in the present        invention, which greatly reduces the overhead of computing the        higher/lower sub-band-edge signals.    -   Difference in the way of generating the complex-type sub-band        signals: In the Rollers algorithm, a real-type filter bank is        employed. Each sub-band signal requires a Hilbert transform or        its approximate operation to generate a complex-type signal for        the subsequent frequency shifting operation. In addition, the        real-type filter bank faces the numerical accuracy issue, i.e.,        higher numerical precision is required as the filter cut-off        frequency is closer to the DC or Nyquist frequency, thus        implementing the filter bank in fixed-point arithmetic with a        lower word length is likely to cause significant distortion. By        contrast, the analysis filter bank 300 of the audio frequency        shifting system 500 employs complex-type filters to generate the        complex-type sub-band signals. Therefore, the frequency shifting        and weighting device 502 does not need to implement Hilbert        transform or its approximate operation, nor does it have to face        the numerical precision issue.    -   Difference in filter bank architecture: In the Rollers        algorithm, each sub-band filter of the filter bank employs a        conventional real-type fourth-order Butterworth filter, where        its gain response possesses a flat passband and fast roll-off        transition bands. By contrast, the audio frequency shifting        system 500 employs the analysis filter bank designed for the        audio frequency shifting system, which reduces the computational        complexity by using paralleled IIR sub-filters and combining the        output signals of these sub-filters. For example, when a        real-type fourth-order Butterworth sub-band filter plus an        all-pass filter for real-to-complex conversion (as in the        Rollers algorithm) is employed, an average of 13 real-type        multiplications are calculated to obtain each sub-band signal.        By contrast, when the aforementioned design of first-order or        second-order binomial weighted analysis filter bank is employed        in the audio frequency shifting system 500, an average of 1 or 2        complex-type multiplications (each corresponds to 4 real-type        multiplications) are calculated to obtain each sub-band signal.        In addition, under the same sub-band width setting, the overall        group delay response of the system, regardless of employing        either the first-order or the second-order binomial weighted        analysis filter bank, is lower than the group delay of the        fourth-order Butterworth-type sub-band filter.    -   Difference on FSC support: Regarding to the Rollers algorithm,        Reference 4 only demonstrates a one-to-one frequency mapping        capability, and directly sums the shifted sub-band signals to        generate the audio output signal. In contrast, the audio        frequency shifting system 500 of the present invention supports        a one-to-many mapping relationship, and the sub-band signals are        weighted in addition to being shifted to adjust the relative        strength of the shifted sub-band signals.

When implementing the audio frequency shifting system 500, it should benoted that:

-   -   If the analysis filter bank 300 employs an equal-width sub-band        configuration, the IIR sub-filters 301 have the same bandwidth        and their filter center frequencies are equally spaced on the        frequency axis. In this way, the values of all b_(k) are        identical and the multiplication of b_(k) can be moved outside        equation (1), e.g., by multiplying the audio input signal by        b_(k) before passing it to the analysis filter bank 300, to        further reduce the computations of the IIR sub-filters 301.    -   The analysis filter bank 300 may employs an unequal-width        sub-band configuration, and the aforementioned filter bank        equations (1) to (10) are still applicable in such        configuration.

In addition to being implemented by a physical device, the functions ofthe audio frequency shifting system 500 can also be implemented by anequivalent computing procedure executed on at least one processor. FIG.9 is a flowchart of an audio frequency shifting procedure of a secondembodiment of the present invention. The flow steps focus on theprocessing method of a segment of a continuous audio signal, because thesignal is segmentally processed for each step to support a real-timeaudio application. In describing the steps of the audio frequencyshifting procedure, equations (11) to (15) and their correspondingparagraphs are referred.

In FIG. 9 , a filter bank computing procedure is executed on at leastone sample of an audio input signal to obtain multiple sub-band signalsand at least one fine input spectrum (step S201). Refer to paragraphs[0022] to [0026] for the filter bank computing procedure.

A plurality of sub-band signal frequencies respectively corresponding tothe sub-band signals are estimated according to each fine inputspectrum, and a plurality of FSPSs corresponding to a plurality ofshifted sub-band signals are determined according to the sub-band signalfrequencies (step S202). More specifically, for each sub-band signal,the envelope of the sub-band signal, the envelope of the lowersub-band-edge signal, and the envelope of the higher sub-band-edgesignal of the fine input spectrum are substituted into equation (11) toestimate the corresponding sub-band signal frequency. Then, the sub-bandsignal frequencies are substituted into a FSC to determine the FSPSs,each of the FSPSs includes a sub-band number, a shift amount, and ashifted sub-band weight. Refer to paragraph [0031] for more detail.

For each FSPS, a frequency shifting operation is performed on one of thesub-band signals corresponding to a sub-band number of the FSPS by ashift amount of the FSPS, and a result of the frequency shiftingoperation is weighted by a shifted sub-band weight of the FSPS to obtainone of the shifted sub-band signals (step S203), which includes at leastone sample. For the detail of frequency shifting and weightingoperation, equation (12) and paragraphs [0033] to [0034] can bereferred. The initial phase of each shifted sub-band signal isdetermined according to the center frequency of the correspondingsub-band.

A sub-band combining operation is performed on the shifted sub-bandsignals to obtain at least one sample of an audio output signal (stepS204). After that, the procedure returns to step S200 for the nextsegment of the audio input signal. Referring to equations (13) to (14)and paragraphs [0035] to [0036], if the shifted sub-band signals are ofequal bandwidth, a plurality of instantaneous samples of the shiftedsub-band signals with zero shift amount and with non-zero shift amountsare summed at each sample period to obtain a zero-shifting sub-bandsummation signal and a non-zero-shifting sub-band summation signalrespectively, and the zero-shifting sub-band summation signal underwenta linear filtering operation and the non-zero-shifting sub-bandsummation signal are added to obtain at least one sample of an audiooutput signal. If the bandwidths of the shifted sub-band signals are notequal, or most (or all) shift amounts of the shifted sub-band signalsare non-zero, a plurality of instantaneous samples of the shiftedsub-band signals at each sample period are summed as equation (15) toobtain at least one sample of the audio output signal.

Although the audio frequency shifting system of the first embodiment andthe audio frequency shifting procedure of the second embodiment employ avery efficient analysis filter bank and a filter bank computingprocedure thereof, their computational complexity is still significantlyhigher than that of the audio frequency shifting systems that employsfrequency-domain signal processing. This is because the fast-computingmethods of the time-to-frequency transforms such as discrete Fouriertransform (hereinafter abbreviated as DFT), short-time Fourier transform(hereinafter abbreviated as STFT), do exist, which achieve an efficiencymuch higher than that of the frequency-division filtering based onfilter banks. Therefore, the audio frequency shifting system based onthe filter bank and the audio frequency shifting procedure based on thefilter bank computing procedure still have room for improvement. Thefollowing embodiment refines the aforementioned filter-bank basedarchitecture to further reduce the computational complexity with thecost of slightly increasing the processing delay.

FIG. 10 is a block diagram of a hybrid audio frequency shifting systemof a third embodiment of the present invention. The hybrid audiofrequency shifting system 1000 comprises a framing and time-to-frequencytransform device 1001, multiple paralleled analysis filter banks 1002, afrequency shifting controller 1003, multiple frequency shifting andweighting devices 1004, and multiple sub-band combiners 1005, and afrequency-to-time transform device 1006.

The framing and time-to-frequency transform device 1001 divides an audioinput signal into multiple audio frames with a frame length of R samplesand a frame spacing of N samples (N≤R/2), and performs an R-pointtime-to-frequency transform (such as STFT, DFT, etc.) on each audioframe to generate one of a plurality of spectrums. The R-pointtime-to-frequency transform is functionally equivalent to separate afull band (from DC to the audio sampling rate f_(SAM)) into Requal-width narrowband signal and decimate the narrowband signals by afactor of N. Therefore, a plurality of bin values of the spectrums at afrequency bin (i.e., corresponding to the same frequency) form one of aplurality of band signals, where the sampling rate of the band signalsis reduced to f_(SAM)/N. If the R-point time-to-frequency transform isan R-point STFT, it can be expressed as:

$\begin{matrix}{{{x_{{BAND},g}\lbrack h\rbrack} = {\sum\limits_{r = 0}^{R - 1}{{x\left\lbrack {{hN} + r} \right\rbrack} \cdot {W_{ANA}(r)} \cdot {\exp\left( {{- j} \cdot \frac{2\pi rg}{R}} \right)}}}},} & (16)\end{matrix}$ ∀g ∈ [0, R − 1]where g denotes the frequency band index, h denotes the frame index,which is also the time index of the band signals, x_(BAND,g) denotes theNo. g band signal, x denotes an audio input signal, W_(ANA)(·) denotesthe analysis window function of the R-point STFT with non-zero valuewhen the input falls within the range of [0, R−1], and the remainingnotations are as aforementioned. The STFT and its inverse transform canrefer to Reference 5. Moreover, since the audio signal is of real type,the audio spectrum values on both sides of the Nyquist frequency areconjugate symmetric. Therefore, the system only needs to calculate oneside of the spectrum, and then take the complex conjugate values to formthe other side of the spectrum. For simplicity, the frequency-domainsignal processing operations can be performed only on the band signalsof No. 0 to R/2.

The analysis filter banks 1002 respectively perform frequency-divisionfiltering and envelope detection on the No. 0 to R/2 band signals togenerate S sub-band signals and No. 0 to R/2 band spectrums in total.For the detail of operation, equations of the analysis filter bank 300in the first embodiment and corresponding paragraphs are referred. Sincethe input of each analysis filter bank in this embodiment is anarrowband band signal, the fine spectrum generated by the analysisfilter banks are referred to as band spectrums to emphasize the narrowfrequency range property. The band spectrums at each frame period arefurther lumped as a fine input spectrum covering the entire frequencyrange of the input signal.

The frequency shifting controller 1003 estimates multiple sub-bandsignal frequencies respectively corresponding to the sub-band signalsaccording to the fine input spectrum, wherein the No. s sub-band signalfrequency can be estimated as:

$\begin{matrix}{{{{\overset{\sim}{f}}_{{SB},s}\lbrack h\rbrack} = {f_{{SB},s} + {C_{{CFO},s} \cdot \frac{{u_{U,s}\lbrack h\rbrack} - {u_{L,s}\lbrack h\rbrack}}{{u_{U,s}\lbrack h\rbrack} + {u_{C,s}\lbrack h\rbrack} + {u_{L,s}\lbrack h\rbrack}}}}},{\forall{s \in \left\lbrack {1,S} \right\rbrack}}} & (17)\end{matrix}$where h denotes the time index of the sub-band signals, and the restnotations are as aforementioned.

Then, the frequency shifting controller 1003 substitutes the sub-bandsignal frequencies into a FSC (allowing one-to-many mapping) forsubsequent frequency shifting operations, wherein the No. s sub-bandsignal is frequency shifted to generate the No. Ŝ_(s-1)+1 to Ŝ_(s)shifted sub-band signal. After the S sub-band signals are frequencyshifted, a total number of S shifted sub-band signals are generated(Ŝ₁=1, Ŝ_(s)≥Ŝ_(s-1)+1, and Ŝ_(s)=Ŝ). In general, the frequency shiftingcontroller 1003 determines S FSPSs respectively corresponding to the Sshifted sub-band signals according to the S sub-band signal frequencies,and each of the FSPSs includes a sub-band number, a shift amount, ashifted sub-band weight, and a shifted band number. In the followingequation, the time index of the FSPSs and the time index of the shiftedsub-band signals are set equal to simplify the representation.

Compared with the FSPSs determined by the frequency shifting controller501 of the first embodiment, each FSPS determined by the frequencyshifting controller 1003 further includes a shifted band number. Thereason is that the frequency shifting range of the frequency shiftingand weighting devices 1004 is reduced to f_(SAM)/N as the sampling rateof the sub-band signals, and the bandwidth of the band signals (i.e.,the upper bound of the bandwidth of the sub-band signals) is reduced tof_(SAM)/R. However, a shift amount specified by the FSC may far exceedf_(SAM)/N or f_(SAM)/R. Therefore, it is necessary to divide thedesignated shift amount into an inter-band shift amount and anintra-band shift amount, where the inter-band shift amount is thedifference between the center frequency of the band after the frequencyshifting and the center frequency of the band before the frequencyshifting, the intra-band shift amount is the designated shift amountminus the inter-band shift amount, and the inter-band shift amountshould minimize the absolute value of the intra-band shift amount. Inaddition, the inter-band shift amount is only for easy explanation. Theequivalent information actually used is the No. of the frequency band towhich a sub-band signal is shifted, which is referred to as shifted bandnumber. Hereinafter an intra-band shift amount is still referred to as ashift amount.

Each of the frequency shifting and weighting devices 1004 correspondingto one of the frequency shift parameter sets performs a frequencyshifting operation on one of the sub-band signals corresponding to asub-band number of the FSPS by a shift amount of the FSPS, and weights aresult of the frequency shifting operation by a shifted sub-band weightof the FSPS to generate one of the shifted sub-band signals. Thefrequency shifting operation and the weighting operation can beexpressed as:

$\begin{matrix}{{{y_{{SHF},v}\lbrack h\rbrack} = {{y_{{FB},s}\lbrack h\rbrack} \cdot {w_{v}\lbrack h\rbrack} \cdot {\exp\left\lbrack {j \cdot \left( {\theta_{v} + {\frac{2\pi N}{f_{SAM}}{\sum\limits_{t = 0}^{h}{f_{{SHF},v}\lbrack t\rbrack}}}} \right)} \right\rbrack}}},{\forall{v \in \left\lbrack {{{\hat{S}}_{s - 1} + 1},{\hat{S}}_{s}} \right\rbrack}},{s \in \left\lbrack {1,S} \right\rbrack}} & (18)\end{matrix}$where the notations are as aforementioned. The initial phase settingθ_(v) of the shifted sub-band signal is the same as in the firstembodiment, which can be determined by the sub-band center frequency ofa corresponding sub-band signal, for example, setting θ_(v) to beproportional to the sub-band number.

Each of the sub-band combiners 1005 performs a sub-band combiningoperation on a subset of the shifted sub-band signals corresponding to ashifted band number to generate one of a plurality of modified bandsignals. Specifically, if the shifted sub-band signals in the subset areof equal bandwidth, the sub-band combiner sums a plurality ofinstantaneous samples of the shifted sub-band signals in the subset withzero shift amount and with non-zero shift amounts at each sample periodto generate a zero-shifting sub-band summation signal and anon-zero-shifting sub-band summation signal respectively. Thezero-shifting sub-band summation signal underwent a linear filteringoperation and the non-zero-shifting sub-band summation signal are addedto generate one of the modified band signals. In this way, the sub-bandcombining operation corresponding to the shifted band number g isexpressed as:

$\begin{matrix}\left\{ {\begin{matrix}{{y_{U,g}\lbrack h\rbrack} = {\sum\limits_{v \in U_{g}}{y_{{SHF},v}\lbrack h\rbrack}}} \\{{y_{v,g}\lbrack h\rbrack} = {\sum\limits_{v \in V_{g}}{y_{{SHF},v}\lbrack h\rbrack}}}\end{matrix},{\forall{g \in \left\lbrack {0,{R/2}} \right\rbrack}}} \right. & (19)\end{matrix}$y_(BAND, g)[h] = y_(U, g)[h] + C_(CMP, g) ⋅ y_(U, g)[h − D_(g)] + y_(v, g)[h],$\begin{matrix}{{D_{g} = {{round}\left( \frac{f_{SAM}}{{N \cdot B}W_{g}} \right)}},{\forall{g \in \left\lbrack {0,{R/2}} \right\rbrack}}} & (20)\end{matrix}$where U_(g) denotes a subset of the numbers of the shifted sub-bandsignals corresponding to shifted band number g and a zero shift amount,and V_(g) denotes a subset of the numbers of the shifted sub-bandsignals corresponding to shifted band number g and non-zero shiftamounts, y_(U,g) denotes the No. g zero-shifting sub-band summationsignal, y_(V,g) denotes the No. g non-zero-shifting sub-band summationsignal, y_(BAND,g) denotes the No. g modified band signal, BW_(g)denotes the bandwidth of the No. g shifted sub-band, C_(CMP,g) denotesan adjustable parameter for the No. g analysis filter bank, and theremaining notations are as aforementioned. The setting of the parameterC_(CMP,g) of (20) is to minimize the fluctuations of the overallresponse of the No. g analysis filter bank.

If there is no shifted sub-band signal in the subset with zero shiftamount, or the bandwidths of the shifted sub-band signals in the subsetwith zero shift amount are not equal, the sub-band combiner sums aplurality of instantaneous samples of the subset of the shifted sub-bandsignals at each sample period to generate one of the modified bandsignals. In this way, the sub-band combining operation can be expressedas a simple summation:

$\begin{matrix}{{{y_{{BAND},g}\lbrack h\rbrack} = {\sum\limits_{v \in {U_{g}\bigcup V_{g}}}{y_{{SHF},v}\lbrack h\rbrack}}},{\forall{g \in \left\lbrack {0,{R/2}} \right\rbrack}}} & (21)\end{matrix}$where the notations are as aforementioned. Moreover, if there is noshifted sub-band signal corresponding to the shifted band number g(i.e., U_(g) and V_(g) in (20) are both empty), the combining operationis not required, and y_(BAND,g)[h]=0 is set.

The frequency-to-time transform device 1006 performs an R-pointfrequency-to-time transform (which is an inverse operation of theR-point time-to-frequency transformation) on a plurality ofinstantaneous samples of the modified band signals at each frame periodto generate an output audio signal. Since the audio spectrum showsconjugate symmetry on both sides of the Nyquist frequency, the complexconjugate values of the modified band signals of the single sidespectrum are used as the modified band signals on the symmetric side ofthe spectrum:y _(BAND,R−g)[h]= y _(BAND,g)[h],∀g∈[1,R/2−1]  (22)The R-point frequency-to-time transform can adopt the weightedoverlap-add method (i.e., an inverse transform of R-point STFT as in(16)) to generate the audio output signal, which can be expressed as:

$\begin{matrix}{{{y_{h}\lbrack n\rbrack} = {\sum\limits_{g = 0}^{R - 1}{{real}\left\{ {{y_{{BAND},g}\lbrack h\rbrack} \cdot {\exp\left( {j \cdot \frac{2\pi gn}{R}} \right)}} \right\}}}},} & (23)\end{matrix}$ $\begin{matrix}{{{y\lbrack n\rbrack} = {\sum\limits_{h = {- \infty}}^{\infty}{{y_{h}\left\lbrack {n - {hN}} \right\rbrack} \cdot {W_{SYN}\left( {n - {hN}} \right)}}}},} & (24)\end{matrix}$where y_(h) denotes the No. h modified signal frame, y denotes the audiooutput signal, W_(SYN)(·) denotes the synthesis window function of theR-point weighted overlap-add method with non-zero value when the inputfalls within the range of [0, R−1], and the remaining notations are asaforementioned.

The hybrid audio frequency shifting system 1000 reduces the samplingrate of each analysis filter bank through inserting the time-frequencytransform pair. Under the condition of equal number of sub-bands, thecomputational complexity of each sub-band of the third embodiment isgreatly reduced compared with that of the first embodiment. On the otherhand, the processing delay of this system is dominated by the groupdelay of the analysis filter banks plus the processing delay of thetime-to-frequency transform and the inverse transform thereof, which isabout one frame period. Since increasing the frame length of thetime-to-frequency transform also increases the processing delay of thesystem, the frame length selection still a trade-off between thecomputational complexity and the processing delay at system level (it isdesired to select an appropriate frame length to reduce thecomputational complexity of the system to approach that of a STFT-basedaudio frequency shifting system, while improve the processing delay ofthe system to an acceptable level). For example, considering that anaudio frequency shifting system of the first embodiment divides theaudio input signal with 12 kHz sampling rate in 128 sub-bands, thealgorithmic delay (10.7 ms) is approximately one-half of the algorithmicdelay of a frequency-domain audio frequency shifting system with asimilar spectral resolution (21.3 ms), while the number of complex-typemultiplications is roughly twenty times of that of the frequency-domainaudio frequency shifting system. However, for the hybrid audio frequencyshifting system of the third embodiment with the similar spectralresolution, the algorithmic delay is about 1˜3 ms higher than that ofthe audio frequency shifting system of the first embodiment (dependingon the frame length setting), and the number of complex-typemultiplications can be reduced to about two to three times of that ofthe frequency-domain audio frequency shifting system. Therefore, it hasconsiderable potential in delay-sensitive applications.

In addition to being implemented by a physical device, the functions ofthe hybrid audio frequency shifting system 1000 can also be implementedby an equivalent computing procedure executed on at least one processor.FIG. 11 is a flowchart of a hybrid audio frequency shifting procedure ofa fourth embodiment of the present invention. In describing the steps ofthe hybrid audio frequency shifting procedure, equations (16) to (24)and their corresponding paragraphs are referred. The flow steps focus onthe processing method of a segment of a continuous audio signal, becausethe signal is segmentally processed for each step to support a real-timeaudio application.

In FIG. 11 , a time-to-frequency transform operation is performed on atleast one frame of an audio input signal to obtain multiple band signalsrespectively corresponding to multiple frequency bands (step S301). Forthe time-to-frequency transform operation, equation (16) and paragraph[0050] can be referred. Each band signal includes at least one spectrumsample corresponding to a frequency band.

A plurality of filter bank computing procedures are executed on aplurality of band signals respectively to obtain a plurality of sub-bandsignals and a plurality of band spectrums, and the band spectrums ateach frame period are lumped as a fine input spectrum (step S302). Referparagraphs [0022] to [0026] and [0051] for the filter bank computingprocedures. Each sub-band signal includes at least one sample.

A plurality of sub-band signal frequencies respectively corresponding tothe sub-band signals are estimated according to the fine input spectrum,and a plurality of FSPSs respectively corresponding to the shiftedsub-band signals are determined according to the sub-band signalfrequencies (step S303). More specifically, for each sub-band signal,the envelope of the sub-band signal, the envelope of the lowersub-band-edge signal, and the envelope of the higher sub-band-edgesignal of the fine input spectrum are substituted into equation (17) toestimate the corresponding sub-band signal frequency. Then, the sub-bandsignal frequencies are substituted into a FSC to determine the FSPSs,each of the FSPSs includes a sub-band number, a shift amount, a shiftedsub-band weight, and a shifted band number. Refer to paragraph [0053]for more detail.

For each FSPS, a frequency shifting operation is performed on one of thesub-band signals corresponding to a sub-band number of the FSPS by ashift amount of the FSPS, and a result of the frequency shiftingoperation is weighted by a shifted sub-band weight of the FSPS to obtainone of the shifted sub-band signals (step S304), which includes at leastone sample. Refer to equation (18) and paragraph [0055] for more detailof the above operations. The initial phase of each shifted sub-bandsignal is determined according to the center frequency of thecorresponding sub-band.

For each of a plurality of shifted band numbers appearing in the FSPSs,a sub-band combining operation on a subset of the shifted sub-bandsignals corresponding to the shifted band number is performed to obtainone of a plurality of modified band signals (step S305), which includesat least one sample. Referring to equations (19) to (20) and paragraphs[0056] to [0057], if the shifted sub-band signals in the subset are ofequal bandwidth, a plurality of instantaneous samples of the shiftedsub-band signals in the subset with zero shift amount and with non-zeroshift amount are summed at each sample period to obtain a zero-shiftingsub-band summation signal and a non-zero-shifting sub-band summationsignal respectively, and the zero-shifting sub-band summation signalunderwent a linear filtering operation and the non-zero-shiftingsub-band summation signal are added to obtain one of the modified bandsignals, which includes at least one sample. If the bandwidths of theshifted sub-band signals in the subset with zero shift amount are notequal, or most (or all) of the shifted sub-band signals in the subsetare with non-zero shift amounts, a plurality of instantaneous samples ofthe shifted sub-band signals in the subset at each sample period aresummed as equation (21) to obtain one of the modified band signals.

A frequency-to-time transform operation is performed on a plurality ofinstantaneous samples of the modified band signals at each frame periodto obtain a plurality of samples of an audio output signal (step S306).After that, the procedure returns to step S300 for the next segment ofthe audio input signal. For the frequency-to-time transform operation,equations (22) to (24) and paragraphs [0057] to [0058] can be referred.

Although the present invention has been described above with referenceto the preferred embodiments and the accompanying drawings, it shall notbe considered as limited. Those skilled in the art can make variousmodifications, omissions and changes to the details of the embodimentsof the present invention without departing from the scope of the claimsof the invention.

What is claimed is:
 1. An analysis filter bank corresponding to aplurality of sub-bands, comprising: a plurality of sub-filters withdifferent center frequencies which perform a plurality of complex-typefirst-order infinite impulse response (IIR) filtering operations on aninput signal to generate a plurality of sub-filter signals; a first setof binomial combiners, each of which performs a weighted-sum operationon a first number of the sub-filter signals with a first set of binomialweights to generate one of a plurality of sub-band signals, wherein thefirst number of the sub-filter signals are generated by the first numberof the sub-filters adjacent in center frequency; a second set ofbinomial combiners, each of which performs a weighted-sum operation on asecond number of the sub-filter signals with a second set of binomialweights to generate one of a plurality of lower sub-band-edge signals orone of a plurality of higher sub-band-edge signals, wherein the secondnumber of the sub-filter signals are generated by the second number ofthe sub-filters adjacent in center frequency; and a plurality ofenvelope detection with decimation devices which perform a plurality ofenvelope detection with decimation operations on the sub-band signals,the lower sub-band-edge signals, and the higher sub-band-edge signals togenerate a plurality of fine spectrums.
 2. The analysis filter bankaccording to claim 1, wherein two of the first set of binomial combinerscorresponding to any two of the sub-bands adjacent in frequency share atleast one of the sub-filter signals.
 3. The analysis filter bankaccording to claim 1, wherein one of the first set of binomial combinersand one of the second set of binomial combiners both corresponding toone of the sub-bands share at least one of the sub-filter signals.
 4. Anaudio frequency shifting system comprising an analysis filter bankaccording to claim 1, wherein the analysis filter bank performsfrequency-division filtering and envelope detection on an input signalto generate a plurality of sub-band signals and a plurality of fineinput spectrums, the audio frequency shifting system further comprising:a frequency shifting controller, which estimates a plurality of sub-bandsignal frequencies respectively corresponding to the sub-band signalsaccording to each of the fine input spectrums, and determines aplurality of frequency shifting parameter sets (FSPSs) respectivelycorresponding to a plurality of shifted sub-band signals according tothe sub-band signal frequencies; a plurality of frequency shifting andweighting devices, each of which corresponding to one of the FSPSsperforms a frequency shifting operation on one of the sub-band signalscorresponding to a sub-band number of the FSPS by a shift amount of theFSPS, and multiplies a result of the frequency shifting operation by ashifted sub-band weight of the FSPS to generate one of the shiftedsub-band signals; and a sub-band combiner, which performs a sub-bandcombining operation on the shifted sub-band signals to generate anoutput signal.
 5. The audio frequency shifting system according to claim4, wherein the sub-band combining operation is to sum a plurality ofinstantaneous samples of the shifted sub-band signals with zero shiftamount and with non-zero shift amounts at each sample period to generatea first signal and a second signal respectively, and to add the firstsignal underwent a linear filtering operation and the second signal togenerate the output signal, or to sum the instantaneous samples of theshifted sub-band signals at each sample period to generate the outputsignal.
 6. The audio frequency shifting system according to claim 4,wherein each of the sub-band signals corresponds to at least one of theshifted sub-band signals.
 7. The audio frequency shifting systemaccording to claim 4, wherein an initial phase of each of the shiftedsub-band signals is determined by a center frequency of one of thesub-bands corresponding to the shifted sub-band signal.
 8. An audiofrequency shifting system comprising a plurality of analysis filterbanks according to claim 1, wherein the analysis filter banksrespectively perform frequency-division filtering and envelope detectionon a plurality of band signals to generate a plurality of sub-bandsignals and a plurality of band spectrums, and the band spectrums ateach frame period are lumped as a fine input spectrum, the audiofrequency shifting system further comprising: a framing andtime-to-frequency transform device, which divides an input signal into aplurality of audio frames with equal frame length and equal framespacing, and performs a time-to-frequency transform on each of the audioframes to generate the band signals; a frequency shifting controller,which estimates a plurality of sub-band signal frequencies respectivelycorresponding to the sub-band signals according to the fine inputspectrum, and determines a plurality of FSPSs corresponding to aplurality of shifted sub-band signals according to the sub-band signalfrequencies; a plurality of frequency shifting and weighting devices,each of which corresponding to one of the FSPSs performs a frequencyshifting operation on one of the sub-band signals corresponding to asub-band number of the FSPS by a frequency shift amount of the FSPS, andmultiplies a result of the frequency shifting operation by a shiftedsub-band weight of the FSPS to generate one of the shifted sub-bandsignals; a plurality of sub-band combiners, each of which performs asub-band combining operation on a subset of the shifted sub-band signalscorresponding to a shifted band number to generate one of a plurality ofmodified band signals; and a frequency-to-time transform device, whichperforms a frequency-to-time transform on a plurality of instantaneoussamples of the modified band signals at each frame period to generate anoutput signal.
 9. The audio frequency shifting system according to claim8, wherein each of the sub-band signals corresponds to at least one ofthe shifted sub-band signals.
 10. The audio frequency shifting systemaccording to claim 8, wherein an initial phase of each of the shiftedsub-band signals is determined by a center frequency of one of thesub-bands corresponding to the shifted sub-band signal.
 11. A filterbank computing procedure corresponding to a plurality of sub-bands,comprising the following steps: performing a plurality of complex-typefirst-order IIR filtering operations with different center frequencieson an input signal to obtain a plurality of sub-filtered signals;selecting a plurality of first subsets of the sub-filtered signals,wherein each of the first subsets corresponding to one of the sub-bandscontains a first number of the sub-filtered signals obtained from thefirst number of the filtering operations adjacent in center frequency,and for each of the first subsets, performing a weighted-sum operationon a plurality of instantaneous values of the first number of thesub-filtered signals in the subset at each sample period with a firstset of binomial weights to obtain one of a plurality of sub-bandsignals; selecting a plurality of second subsets of the sub-filteredsignals, wherein each of the second subsets corresponding to alower-frequency side or a higher-frequency side of one of the sub-bandscontains a second number of the sub-filtered signals obtained by thesecond number of the filtering operations adjacent in center frequency,and for each of the second subsets, performing a weighted-sum operationon a plurality of instantaneous values of the second number of thesub-filtered signals in the subset at each sample period with a secondset of binomial weights to obtain one of a plurality of lowersub-band-edge signals or one of a plurality of higher sub-band-edgesignals; and performing a plurality of envelope detection withdecimation operations on the sub-band signals, the lower sub-band-edgesignals, and the higher sub-band-edge signals to obtain at least onefine spectrum.
 12. An audio frequency shifting procedure, whichcomprises a step of executing a filter bank computing procedureaccording to claim 11 on an input signal to obtain a plurality ofsub-band signals and at least one fine input spectrum, the audiofrequency shifting procedure further comprises the following steps:estimating a plurality of sub-band signal frequencies respectivelycorresponding to the sub-band signals according to each of the at leastone fine input spectrum, and determining a plurality of FSPSscorresponding to a plurality of shifted sub-band signals according tothe sub-band signal frequencies; for each of the FSPSs, performing afrequency shifting operation on one of the sub-band signalscorresponding to a sub-band number of the FSPS by a shift amount of theFSPS, and multiplying a result of the frequency shifting operation by ashifted sub-band weight of the FSPS to obtain one of the shiftedsub-band signals; and performing a sub-band combining operation on theshifted sub-band signals to obtain an output signal.
 13. The audiofrequency shifting procedure according to claim 12, wherein the sub-bandcombining operation is to sum a plurality of instantaneous samples ofthe shifted sub-band signals with zero shift amount and with non-zeroshift amounts at each sample period to obtain a first signal and asecond signal respectively, and to add the first signal underwent alinear filtering operation and the second signal to generate the outputsignal, or to sum the instantaneous samples of the shifted sub-bandsignals at each sample period to obtain the output signal.
 14. The audiofrequency shifting procedure according to claim 12, wherein each of thesub-band signals corresponds to at least one of the shifted sub-bandsignals.
 15. The audio frequency shifting procedure according to claim12, wherein an initial phase of each of the shifted sub-band signals isdetermined by a center frequency of one of the sub-bands correspondingto the shifted sub-band signal.
 16. An audio frequency shiftingprocedure, which comprises a step of executing a plurality of filterbank computing procedures according to claim 11 respectively on aplurality of band signals to obtain a plurality of sub-band signals anda plurality of band spectrums, and lumping the band spectrums at eachframe period as a fine input spectrum, the audio frequency shiftingprocedure further comprises the following steps: performing atime-to-frequency transform operation on at least one frame of an inputsignal to obtain the band signals; estimating a plurality of sub-bandsignal frequencies respectively corresponding to the sub-band signalsaccording to the fine input spectrum, and determining a plurality ofFSPSs respectively corresponding to a plurality of shifted sub-bandsignals according to the sub-band signal frequencies; for each of theFSPSs, performing a frequency shifting operation on one of the sub-bandsignals corresponding to a sub-band number of the FSPS by a shift amountof the FSPS, and multiplying a result of the frequency shiftingoperation by a shifted sub-band weight of the FSPS to obtain one of theshifted sub-band signals; for each of a plurality of shifted bandnumbers appearing in the FSPSs, performing a sub-band combiningoperation on a subset of the shifted sub-band signals corresponding tothe shifted band number to obtain one of a plurality of modified bandsignals; and performing a frequency-to-time transform operation on aplurality of instantaneous samples of the modified band signals at eachframe period to obtain an output signal.
 17. The audio frequencyshifting procedure according to claim 16, wherein each of the sub-bandsignals corresponds to at least one of the shifted sub-band signals. 18.The audio frequency shifting procedure according to claim 16, wherein aninitial phase of each of the shifted sub-band signals is determined by acenter frequency of one of the sub-bands corresponding to the shiftedsub-band signal.